The way I would have done it is this: is the same as . Now, that can change from "> 0" to "< 0" only where the numerator, 4x- 13, is equal to 0 (so the fraction is 0) or where x- 3= 0 (where the fraction is "discontinuous"). The sign is constant on the intervals , , and . If x= 0, which is less than 3, . If x= 4, which is larger than 13/4, . If x= 3.1, which is between 3 and , .

The way I would have done it is this: is the same as . Now, that can change from "> 0" to "< 0" only where the numerator, 4x- 13, is equal to 0 (so the fraction is 0) or where x- 3= 0 (where the fraction is "discontinuous"). The sign is constant on the intervals , , and . If x= 0, which is less than 3, . If x= 4, which is larger than 13/4, . If x= 3.1, which is between 3 and , .

Re: Inequality

Originally Posted by veileen

The second method is wrong. You don't know if or .

sorry for bringing up an old thread, but I thought about this inequality thing again, looking over what you wrote isn't always?, isn't this true for all real numbers x, for example sub in x=5 then the answer would be 2, which is 5-3, if subbing in lets say a negative number -1, then it would be 16/-4=-1-3 which is true again, the same is true for x=0 or a positive number smaller than 3, eg 1

Re: Inequality

"If you test some points you will get" Absolutely wrong. In general, you learn math for not testing things - anybody can do that.

There are a lot of things that anybody can do- that doesn't mean it is wrong.

The only places an inequality can change form ">" to "<" is where the function is 0 or is not continuous. For fractions that is where the numerator is 0 or where the denominator is 0. Once you have found those points, checking one point in each interval tells you which. What TheEmptySet said was perfectly valid.